As soon as the handover is proposed, and well before the authorized period is close to expiring. The length of the handover is set by the employer's needs; the length of permitted stay is not, and the second one governs.
Work backwards from the authorized end date
Take the date on the admission record and count back far enough to gather a revised letter, obtain legal review, and complete whatever step applies. If that leaves no room, the honest answer may be a shorter handover or a different arrangement rather than a rushed filing. Avoid booking the successor's start date around an outcome that has not been confirmed.
Productive work does not become permissible merely because no wage is paid or the employer calls it testing.
An employer-filed petition on Form I-129 sits in a USCIS queue unless premium processing is used. Raising the extension question early is also the moment to revisit whether the stay still reads as genuinely temporary, since repeated renewals alone do not settle that question one way or the other and a pattern is easier to explain while it is still short. Ask counsel to review any change in circumstances since the last renewal, a home purchase, a long lease, or a shift in stated plans, that could affect how the current request is read. Address that question well before the filing itself, not as an afterthought once the paperwork is otherwise ready. Treat the timing conversation as covering both the calendar and the underlying intent, since either one alone leaves the request incomplete.